COLLEGE PHYSICS
2nd Edition
ISBN: 9781464196393
Author: Freedman
Publisher: MAC HIGHER
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Chapter 26, Problem 15QAP
To determine
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=
Using the formula for the hydrogen atom energy levels, En
constant can be written in terms of fundamental quantities,
RH
=
Me 4
8€ ²h³c
Me4
1
860²h² n²¹
the Rydberg
and its value approaches, RH → R = 10,973,731.6 m¹ in the limit μ→ me.
(a) How would this constant be defined for a one-electron species containing Z protons in
its nucleus? Consider how this changes the form of the Hamiltonian and the energy
levels for that Hamiltonian.
(b) The hydrogen atom emission lines in the Balmer series (n₂ = 2) lie in the visible portion of
the electromagnetic spectrum. Would this also be true if Z> 1? Find the wavelength (in
nm) of the n = 32 emission in hydrogen and that for a one-electron species with Z = 2.
(You will be asked to report a quantity on the quiz that depends on these two values.)
Select all of the following statements that are basic assumptions of the Bohr model of the atom.
A) Atoms have a central nucleus with electrons in orbit about this nucleus.
B) Atoms are solid spheres of matter.Atoms are made of positive material with electrons fixed in place in this positive material.
C) Electrons orbit the nucleus, but the orbits can have only certain sizes and energy values.
D) Electrons can jump from one orbit to another around the nucleus.
E) They must gain energy to jump to a higher level, and they release energy when jumping to a lower level.
Which atomic picture (named after the respective physicists) gives the most complete
and accurate picture of how electrons act within atoms?
O None of these are correct.
O Bohr
O de Broglie
O Schrödinger
Chapter 26 Solutions
COLLEGE PHYSICS
Ch. 26 - Prob. 1QAPCh. 26 - Prob. 2QAPCh. 26 - Prob. 3QAPCh. 26 - Prob. 4QAPCh. 26 - Prob. 5QAPCh. 26 - Prob. 6QAPCh. 26 - Prob. 7QAPCh. 26 - Prob. 8QAPCh. 26 - Prob. 9QAPCh. 26 - Prob. 10QAP
Ch. 26 - Prob. 11QAPCh. 26 - Prob. 12QAPCh. 26 - Prob. 13QAPCh. 26 - Prob. 14QAPCh. 26 - Prob. 15QAPCh. 26 - Prob. 16QAPCh. 26 - Prob. 17QAPCh. 26 - Prob. 18QAPCh. 26 - Prob. 19QAPCh. 26 - Prob. 20QAPCh. 26 - Prob. 21QAPCh. 26 - Prob. 22QAPCh. 26 - Prob. 23QAPCh. 26 - Prob. 24QAPCh. 26 - Prob. 25QAPCh. 26 - Prob. 26QAPCh. 26 - Prob. 27QAPCh. 26 - Prob. 28QAPCh. 26 - Prob. 29QAPCh. 26 - Prob. 30QAPCh. 26 - Prob. 31QAPCh. 26 - Prob. 32QAPCh. 26 - Prob. 33QAPCh. 26 - Prob. 34QAPCh. 26 - Prob. 35QAPCh. 26 - Prob. 36QAPCh. 26 - Prob. 37QAPCh. 26 - Prob. 38QAPCh. 26 - Prob. 39QAPCh. 26 - Prob. 40QAPCh. 26 - Prob. 41QAPCh. 26 - Prob. 42QAPCh. 26 - Prob. 43QAPCh. 26 - Prob. 44QAPCh. 26 - Prob. 45QAPCh. 26 - Prob. 46QAPCh. 26 - Prob. 47QAPCh. 26 - Prob. 48QAPCh. 26 - Prob. 49QAPCh. 26 - Prob. 50QAPCh. 26 - Prob. 51QAPCh. 26 - Prob. 52QAPCh. 26 - Prob. 53QAPCh. 26 - Prob. 54QAPCh. 26 - Prob. 55QAPCh. 26 - Prob. 56QAPCh. 26 - Prob. 57QAPCh. 26 - Prob. 58QAPCh. 26 - Prob. 59QAPCh. 26 - Prob. 60QAPCh. 26 - Prob. 61QAPCh. 26 - Prob. 62QAPCh. 26 - Prob. 63QAPCh. 26 - Prob. 64QAPCh. 26 - Prob. 65QAPCh. 26 - Prob. 66QAPCh. 26 - Prob. 67QAPCh. 26 - Prob. 68QAPCh. 26 - Prob. 69QAPCh. 26 - Prob. 70QAPCh. 26 - Prob. 71QAPCh. 26 - Prob. 72QAPCh. 26 - Prob. 73QAPCh. 26 - Prob. 74QAPCh. 26 - Prob. 75QAPCh. 26 - Prob. 76QAPCh. 26 - Prob. 77QAPCh. 26 - Prob. 78QAPCh. 26 - Prob. 79QAPCh. 26 - Prob. 80QAPCh. 26 - Prob. 81QAPCh. 26 - Prob. 82QAPCh. 26 - Prob. 83QAPCh. 26 - Prob. 84QAPCh. 26 - Prob. 85QAPCh. 26 - Prob. 86QAPCh. 26 - Prob. 87QAPCh. 26 - Prob. 88QAPCh. 26 - Prob. 89QAPCh. 26 - Prob. 90QAPCh. 26 - Prob. 91QAPCh. 26 - Prob. 92QAPCh. 26 - Prob. 93QAPCh. 26 - Prob. 94QAPCh. 26 - Prob. 95QAPCh. 26 - Prob. 96QAPCh. 26 - Prob. 97QAPCh. 26 - Prob. 98QAPCh. 26 - Prob. 99QAPCh. 26 - Prob. 100QAPCh. 26 - Prob. 101QAPCh. 26 - Prob. 102QAPCh. 26 - Prob. 103QAPCh. 26 - Prob. 104QAP
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- Look up the values of the quantities in aB=h242mekqe2, and verify that the Bohr radius aB is 0.5291010 m.arrow_forwardExplain why spectral lines of the hydrogen atom are split by an external magnetic field. What determines the number and spacing of these lines?arrow_forwardWhich of the following is not true of BohrOs atomic model? O The electron in the orbit nearest to the nucleus has the lowest energy. O The Coulomb force between the nucleus and the electron maintains the electron in orbit. h O The angular momentum of an electron in the allowed orbit is equal to an integral multiple of O Radiation is emitted when an electron orbits in the allowed orbit.arrow_forward
- 8-1. Show that the atomic unit of energy can be written as ħ² e² ma Απερβο En = me 16π εjhtarrow_forwardFor an object orbiting the sun, such as a planet, comet, or asteroid, is there any restriction on the z-component of its orbital angular momentum such as there is with the z-component of the electron’s orbital angular momentum in hydrogen? Explain.arrow_forwardAssuming that only a single electron is present and a Bohr model, calculate the mean radius, orbital velocity, and energy of a N=1 electron of hydrogen N=4 electron for lead N=1 electron for plutonium N=1 electron for an element with Z = 142arrow_forward
- a) Find: [Sx, S.] and [L-,x] b) Which of these wave functions are not allowed in hydrogen atom: P2,1,1 • P3,1,1 • P2,0,-1 , P3,2,-2 c) L./@320 > = d) S-/x. >=arrow_forwardThe gravitational attraction between electron and proton in a hydrogen atom is weaker than the coulomb attraction by a factor of about 10-40. An alternative way of looking at this fact is to estimate the radius of the first Bohr orbit of a hydrogen atom if the electron and proton were bound by gravitational attraction. You will find the answer interesting.arrow_forwardCalculate the radius of second Bohr orbit in hydrogen atom from the given data. Mass of electron = 9.1 × 1031 kg %3D Charge on the electron = 1.6 × 101º C %3D Plank's constant = 6.63 × 10“ J.S. %3D Permitivity of free space = 8.85 x 10-12 C/Nm² %3Darrow_forward
- Assume that in the Stem-Gerlach experiment as described for neutral silver atoms,the magnetic field B has a magnitude of 0.25 T. Calculate the energy difference between the magnetic moment orientations of the silver atoms in the two sub beams? a)111.97 Ghz b)83.98 Ghz c)7.00 Ghz d)20.99 Ghz e)41.99 Ghzarrow_forward(c) Consider the semi-classical model for a two-electron atom illustrated in the diagram below. This model attempts to extend the Bohr model to a two-electron system by assuming both electrons follow a circular orbit around the nucleus while remaining diametrically opposite to each other. electron nucleus, electron (i) Carefully explain why, for the ground state of helium, this semi-classical model predicts that both electrons would experience an effective nuclear charge Zeff %3D (ii) Assuming that each electron's angular momentum is quantized in the same manner as the usual Bohr model for single-electron atoms, calculate the total binding energy of the ground state of helium according to this semi classical model.arrow_forwardExplain the physics behind the fourth assumption in Bohr's atomic model, i.e., mevr-nh/2, where me and v are the mass and velocity of electron around the nucleus, respectively, r is the radius of an allowed orbit, n is an integer and h is the Plank constant.arrow_forward
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